Just a few ideas:-
Will the log require electronic signature by the PI if there is no longer a wet ink signature. Obviously it is a problem if passwords are shared such that others could have writing rights, this process should be made very secure indeed with identification of the author.

Also you need to plan for “read-only” access for Inspectors (readily available and freely accessible) as well as monitors/auditors.
How is “read-only” access maintained?
How is the log maintained so that no unauthorised changes are made?
Is the log and audit trail [of all changes and accesses (etc)] maintained securely and always available together (i.e. log and audit trail always bound together)? When the delegation log is archived by the investigator/institution (and also the sponsor copy archived with the sponsor) will they be archive according to GCP requirements and be readily available and readable for 25 years?
Making sure that the audit trail of the log, is readily available and easily accessible in a “read-only” format for monitors/auditors/inspectors to see on their visits.

Surely only the PI can approve the delegation of a trial related task? The PIs is required to perform all tasks themselves, unless they delegate tasks (& document PI oversight) to appropriate team personnel, who are documented as being qualified by education, training and experience, to carry out those tasks.
Make sure that the PI not only prospectively and contemporaneously approves properly qualified and TRAINED team members, but also rescind/withdraw that delegation if personnel are non-compliant or are no longer performing that task. It is often found that personnel are delegated a task, but never have that duty withdrawn from them even when they are no longer working on the trial.

If it is also combined with a signature log then there will be other concerns about access and secure authentication. Will there be any paper documentation? If so then there may be a need for both a paper (wet ink) signature log as well as an electronic one.

Documented oversight of all trial personnel and tasks is vitally important (see ICH E 6 R2).